• Communications of the Korean Mathematical Society
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• v.22 no.4
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• pp.553-564
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• 2007

In this paper we establish several integration by parts formulas involving integral transforms of functionals of the form $F(y)=f(<{\theta}_1,\;y>),\ldots,<{\theta}_n,\;y>)$ for s-a.e. $y{\in}C_0[0,\;T]$, where $<{\theta},\;y>$ denotes the Riemann-Stieltjes integral ${\int}_0^T{\theta}(t)\;dy(t)$.

• Kyungpook Mathematical Journal
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• v.56 no.1
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• pp.173-184
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• 2016

Mock theta functions are the most interesting topic mentioned in Ramanujan's Lost Notebook, due to its emerging application in the field of Number theory, Quantum invariants theory and etc. In the present research articles we have made an attempt to develop continued fractions representation of all the existing Mock theta functions.

• Communications of the Korean Mathematical Society
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• v.18 no.1
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• pp.127-131
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• 2003

Let X$_1$, X$_2$,... be a sequence of independent and identically distributed random variables with continuous cumulative distribution function F(x). X$_j$ is an upper record value of this sequence if X$_j$ > max {X$_1$,X$_2$,...,X$_{j-1}$}. We define u(n)=min{j$\mid$j> u(n-1), X$_j$ > X$_{u(n-1)}$, n $\geq$ 2} with u(1)=1. Then F(x) = 1-x$^{\theta}$, x > 1, ${\theta}$ < -1 if and only if (${\theta}$+1)E[X$_{u(n+1)}$$\mid$X$_{u(m)}$=y] = ${\theta}E[X_{u(n)}$\mid$X_{u(m)}=y], (\theta+1)^2E[X_{u(n+2)}$\mid$X_{u(m)}=y] = \theta^2E[X_{u(n)}$\mid$X_{u(m)}=y], or (\theta+1)^3E[X_{u(n+3)}$\mid$X_{u(m)}=y] = \theta^3E[X_{u(n)}$\mid$X_{u(m)}=y], n $\geq$ M+1$.

• Journal of the Korean Statistical Society
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• v.19 no.2
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• pp.182-185
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• 1990

Let a p-component vector y have a p-variate normal distribution $N(b\theta, \Sigma), \Sigma$ unknown, b specified, then for testing $\theta = 0$ against general $\theta$, Khatri and Rao (1987) derive a certain t test and obtain its power function. This paper presents a direct derivation of this power function in terms of the original variates unlike Khatri and Rao (1987) who resort to the canonical transformations of the original variates and the conditional distributions.

• Korean Journal of Applied Biomechanics
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• v.25 no.3
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• pp.241-248
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• 2015

Objective : The purpose of this study was to investigate the theta on the components of ground reaction force according to the ground conditions during gait. Method : Six healthy women(mean age: 22 yrs, mean height: $166.14{\pm}2.51cm$, mean body weights: $56.61{\pm}4.58kg$) participated in this study. The medial-lateral GRF(Fx 1), anterior-posterior GRF(Fy 1, Fy 2), vertical GRF(Fz 1, Fz 2, Fz 3), and impact loading rate were determined from time function and frequency domain. Also, GRF theta were time function and forces. Results : Fx 1, Fy 1 and Fy 2 of stair descending showed significant statistically higher forces than that of level walking, and ascending. Fz 1 of stairs descending showed significant statistically higher forces than that of level walking and stairs ascending(theta $88.62^{\circ}$). Also, Fz 2 of level walking showed significant statistically higher forces than that of stairs ascending and descending(theta $65.78^{\circ}$). Fz 3 of stairs ascending showed significant statistically higher forces than that of level walking and stairs descending($65.26^{\circ}$). Impact loading rate of stairs descending showed significant statistically higher forces than that of level and ascending walking. The GRF showed similar correlation with GRF theta(r=.603) according to the ground conditions during gait. Conclusion : These results suggest that the GRF theta can be used in conjunction with a gait characteristics, prediction of loading rate and dynamic stability.

• 한국해양학회지
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• v.5 no.2
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• pp.41-51
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• 1970

Periodic characters of water temperature in the regions of the Mishima and the Okinoshima were derived through the analysis of the five days interval data during 1914 to 1970 mainly. In terms of ten days mean temperatures, annual variation function of the Mishima region, Korea Strait, is F($\theta_d$)=17.45-5.34 cos $\theta_d$-3.77 sin $\theta_d$+0.62 sin $2\theta_d$ -0.52 sin $3\theta_d$, where $\theta_d$=$\frac{\pi}{18}$(d-2), d is the order of ten days period 1 to 36. And in the region of Okinoshima, Tsushima Strait, we find F($\theta_d$)=18.88-5.39 cos $\theta_d$-3.60 sin $\theta_d$+0.52 sin $2\theta_d$. The annual mean temperature is 17.4$^{\circ}C$ in the Mishima region, 18.9$^{\circ}C$ in the Okinoshima region, and the amplitudes of annual variation functions are 7$^{\circ}C$ in both regions with minimum temperature in the middle ten days of February, maximum in the middle ten days of August. The long term variations of surface water temperature with 12 5 years period were observed in the annual mean temperature, monthly mean temperatures and the fixed day temperatures of every year. In addition to these, relatively short term variations were also found significant periods of 3 years, 4 years and 2 years, respectively.

• Communications of the Korean Mathematical Society
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• v.37 no.1
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• pp.31-43
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• 2022

In his notebooks, Srinivasa Ramanujan recorded several modular equations that are useful in the computation of class invariants, continued fractions and the values of theta functions. In this paper, we prove some new modular equations of signature 2 by well-known and useful theta function identities of composite degrees. Further, as an application of this, we evaluate theta function identities.

• Journal of Society of Preventive Korean Medicine
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• v.4 no.2
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• pp.214-234
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• 2000

This study was carried to identify whether acupuncture of several acupuncture points can affect the brain and to observe which aspects appear in EEG mapping, using electroencephalography. Those results are as follows ; 1. The pattern of resting computerized EEG map in intact human is appered normal 2. Each Acupuncture in Kwan Weon or Jog Sam Ri meridian points bring about the increase in $\theta,\;\alpha-wave$ activity and at various area of the cerebrium and the decrease in $\delta,\;\beta-wave$ activity. It strands to reason that brain function is elevated On the other hand , synchronous acupuncture bring about the decrease of brain function in view of the decrease of $\delta,\;\theta-wave$ activity at frontal area, and the unstable brain state in view of the increase of $\beta-wave$ activity. 3. Acupuncture in Hyeon Jong meridian point bring about the increase of $\delta,\;\theta-wave$ activity at frontal area and $\beta-wave$ activity at temporal area. From these we deduce that brain function is declined and brain is unstable. Synchronous acupuncture with other meridian points reversly showed that brain function is elevated. 4. Synchronous acupuncture in Kwan Weon , Jog Sam Ri, Hyeon Jong bring about the decrease of the brain function and the unstable brain state, showing the pattern of increased $\delta,\;\theta-wave$ activity at frontal, parietal area, and increased $\beta-wave$ activity at temporal area.

• Journal of the Chungcheong Mathematical Society
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• v.21 no.2
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• pp.269-278
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• 2008

Let ${\partial}D$ be the boundary of the open unit disk D in the complex plane and $L^p({\partial}D)$ the class of all complex, Lebesgue measurable function f for which $\{\frac{1}{2\pi}{\int}_{-\pi}^{\pi}{\mid}f(\theta){\mid}^pd\theta\}^{1/p}<{\infty}$. Let P be the orthogonal projection from $L^p({\partial}D)$ onto ${\cap}_{n<0}$ ker $a_n$. For $f{\in}L^1({\partial}D)$, ${\hat{f}}(z)=\frac{1}{2\pi}{\int}_{-\pi}^{\pi}P_r(t-\theta)f(\theta)d{\theta}$ is the harmonic extension of f. Let ${\hat{P}}$ be the composition of P with the harmonic extension. In this paper, we will show that if $1, then ${\hat{P}}:L^p({\partial}D){\rightarrow}H^p(D)$ is bounded. In particular, we will show that ${\hat{P}}$ is unbounded on $L^{\infty}({\partial}D)$.

• Journal of Korean Ophthalmic Optics Society
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• v.10 no.4
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• pp.273-281
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• 2005

The weight of spectacles fined on is resolved into its components along the nose's slide plane and the normal to the nose plane where the nosepad is located. The equation and its numerical solution to determine the component force was derived as a function of splay angle ${\Psi}$, $sin{\Psi}$, $cos{\Psi}$, and $cot{\Psi}$, incorporated with ${\theta}$ and ${\Phi}$, the angles viewed from side and front of the face, respectively. Values of inclination angle ${\theta}$ and ${\Phi}$ could be obtained to fulfill the condition where the frictional force between the nose and pad is either greater than the normal pressure exerted by the spectacles on the nose. With the value of ${\theta}$ fixed the normal pressure increases as ${\Phi}$ increases. With ${\Phi}$ fixed, the effect of ${\theta}$ is the same.